Shuffling Pi/Fst/Theta/D

Find significantly different loci/regions between years using shuffling to create null distributions

source("../Rscripts/BaseScripts.R")
require(data.table)
require(plyr)
require(RColorBrewer)

1 Theta null distribution

1.1 Create persite theta.pest.gz files in angsd

```bash

/home/jamcgirr/apps/angsd/misc/thetaStat  print /home/ktist/ph/data/angsd/theta/PWS91_maf00.thetas.idx | gzip > /home/ktist/ph/data/angsd/theta/PWS91_maf00_thetas.pestPG.gz

# Run printTheta.sh at farm

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## Run R scripts at farm to create null distribution of genome-wide thetas

Run angsd_theta_siteshuffle_null.sh at farm, which runs Pi_shuffle_pws.R 
 - Takes long time, so create a script for each pop.year combination and run separately 

Output from theta shuffling results are in Data/shuffle/theta.siteshuffle.50000.PWS91_PWS96.csv.gz


## Calculate p-values for differences in theta, pi, and Tajima's D using the results from shuffling 


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```r
#from codEvol angsd_theta_siteshuffle_null_stats.R

###########################
# load functions
###########################
require(data.table)
require(plyr)
require(ggplot2)
require(RColorBrewer)


#####################
# read in and prep data
#####################

years<-c("PWS91","PWS96","PWS07","PWS17")
comb<-t(combn(years, 2))

chrmax <- fread('../Data/new_vcf/chr_sizes.bed')
chrmax<-chrmax[,-2]
colnames(chrmax)<-c("chr", "len")
chrmax$start<-c(0,cumsum(chrmax$len)[1:(nrow(chrmax)-1)])

chrmax$end<-cumsum(chrmax$len)
chrmax$middle<-(chrmax$end-chrmax$start)/2+chrmax$start

#setkey(chrmax, chr)

#Functions to calculate p-values from codEvol
calcpG <- function(thetachange, null){ # for increases in theta
  return((sum(null > thetachange)+1)/(length(null)+1)) # equation from North et al. 2002 Am J Hum Gen
}
calcpL <- function(thetachange, null){ # for decreases in theta
  return((sum(null < thetachange)+1)/(length(null)+1)) # equation from North et al. 2002 Am J Hum Gen
}


ch_cols <- brewer.pal(4, 'Paired')[rep(1:2,13)]
Datall<-data.table()
for (p in 1: nrow(comb)){
    # max theta per genome from reshuffling (all sites) from angsd_theta_siteshuffle_null.r
    null<-fread(paste0('../Data/shuffle/theta.siteshuffle.50000.', comb[p,1],"_",comb[p,2],'.csv.gz'))
    
    #upper and lower 95%
    null[, .(tWd_l95 = quantile(mintWd, 0.05), tWd_u95 = quantile(maxtWd, probs = 0.95),
                tPd_l95 = quantile(mintPd, 0.05), tPd_u95 = quantile(maxtPd, probs = 0.95),
                tDd_l95 = quantile(mintDd, 0.05), tDd_u95 = quantile(maxtDd, probs = 0.95))]

    #assign(paste0("null.",comb[p,1],"_",comb[p,2]), null)    
    
    # sliding windows theta change (GATK sites) from angsd_theta_siteshuffle_null.r
    dat<-fread(paste0('../Data/shuffle/theta_change_region_50000.', comb[p,1],"_",comb[p,2],'.csv.gz'), drop = 1)
    dat[,pop:=paste0(comb[p,1],"_",comb[p,2])]
    
    dat<-merge(dat, chrmax[,c("chr","start")], by.x="Chromo", by.y = "chr")
    dat[, POSgen := WinCenter + start]
    dat[,start := NULL] #remove start
    
    #calculate p-values
    #1. thetaW loci
    dat[tWd > 0, tWd.p := calcpG(tWd, null$maxtWd), by = .(Chromo, WinCenter)] # thetaW  loci
    dat[tWd <= 0, tWd.p := calcpL(tWd, null$mintWd), by = .(Chromo, WinCenter)]
    #2. theta pi
    dat[tPd > 0, tPd.p := calcpG(tPd, null$maxtPd), by = .(Chromo, WinCenter)] # theta pi
    dat[tPd <= 0, tPd.p := calcpL(tPd, null$mintPd), by = .(Chromo, WinCenter)]
    
    #Tajima's D
    dat[tDd > 0, tDd.p := calcpG(tDd, null$maxtDd), by = .(Chromo, WinCenter)] # tajima's D
    dat[tDd <= 0, tDd.p := calcpL(tDd, null$mintDd), by = .(Chromo, WinCenter)]

    write.csv(dat, file=gzfile(paste0('../Output/Pi/Shuffle/theta_siteshuffle_', comb[p,1],"_",comb[p,2],'.csv.gz')))
    
    Datall<-rbind(Datall, dat)
}

write.csv(Datall, file=gzfile(paste0('../Output/Pi/Shuffle/theta_siteshuffle_PWS_summary.csv.gz')))

1.2 Plot the results

1.2.1 Changes in Pi/Theta/D between years

## Plot the results ##
Datall<-fread('../Output/Pi/Shuffle/theta_siteshuffle_PWS_summary.csv.gz')

winsz = 5e4 

#Changes in Pi between years
Datall$Chromo<-factor(Datall$Chromo, levels=c(paste0("chr",1:26)))
Datall$pop<-factor(Datall$pop, levels=c("PWS91_PWS96","PWS91_PWS07","PWS91_PWS17","PWS96_PWS07","PWS96_PWS17","PWS07_PWS17"))
ch_cols <- brewer.pal(4, 'Paired')[rep(1:2,13)]
ggplot(Datall, aes(POSgen, tPd/winsz, color = Chromo)) + 
    geom_point(size = 0.5, alpha = 0.3) +
    facet_wrap(~pop, ncol = 1) +
    scale_color_manual(values = ch_cols, guide="none") +
    ylab('Change in pi per site')+xlab("Chromosome")+
    ggtitle("Changes in Pi")+
    scale_x_continuous(breaks=chrmax$middle, labels=1:26)+
    theme_bw()
ggsave(paste0('../Output/Pi/Shuffle/Changes_in_Pi_PWS.png'), width = 7.5, height = 9, dpi = 300)

# plot theta_Watterson change
ggplot(Datall, aes(POSgen, tWd/winsz, color = Chromo)) + 
  geom_point(size = 0.5, alpha = 0.3) +
  scale_color_manual(values = ch_cols, guide="none") +
    facet_wrap(~pop, ncol = 1) +
  ylab('Change in Wattersons theta per site')+xlab("Chromosome")+
  ggtitle("Changes in Pi")+
    scale_x_continuous(breaks=chrmax$middle, labels=1:26)+
    theme_bw()
ggsave('../Output/Pi/Shuffle/Changes_in_thetaW_PWS.png', width = 7.5, height = 9, dpi = 300)

# plot Tajima's D change
ggplot(Datall, aes(POSgen, tDd, color = Chromo)) + 
    geom_point(size = 0.5, alpha = 0.3) +
    scale_color_manual(values = ch_cols,guide="none") +
    facet_wrap(~pop, ncol = 1) +
    ylab('Change in Tajimas D per window')+xlab("Chromosome")+
    ggtitle("Changes in Tajima's D")+
    scale_x_continuous(breaks=chrmax$middle, labels=1:26)+
    theme_bw()
ggsave('../Output/Pi/Shuffle/Changes_in_TajimasD_PWS.png', width = 7.5, height = 9, dpi = 300)

1.2.2 Plot the p-values for differences in P/Theta along the genome

# plot pi p-value vs. position 
ch_cols <- brewer.pal(4, 'Paired')[rep(1:2,13)]
Datall$Chromo<-factor(Datall$Chromo, levels=c(paste0("chr",1:26)))
Datall$pop<-factor(Datall$pop, levels=c("PWS91_PWS96","PWS91_PWS07","PWS91_PWS17","PWS96_PWS07","PWS96_PWS17","PWS07_PWS17"))

ggplot(Datall, aes(POSgen, -log10(tPd.p)*sign(tPd), color = Chromo)) + 
    geom_point(size = 0.4, alpha = 0.3) +
    facet_wrap(~pop, ncol = 1) +
    scale_color_manual(values = ch_cols, guide="none") +xlab("Chromosome")+
    ylab("log10(P-value)")+
    geom_hline(yintercept = log10(0.05), linetype = 'dashed', color = 'red',size=0.3) +
    geom_hline(yintercept = -log10(0.05), linetype = 'dashed', color = 'red', size=0.3)+
    ggtitle("P-values for changes in Pi")+
    scale_x_continuous(breaks=chrmax$middle, labels=1:26)+
    theme_bw()
ggsave('../Output/Pi/Shuffle/Changes_in_Pi.siteshuffle.p-values_PWS.png', width = 7.5, height =11, units = 'in', dpi = 300)


# plot thetaW p-value vs. position (all loci)
ggplot(Datall, aes(POSgen, -log10(tWd.p)*sign(tWd), color = Chromo)) + 
  geom_point(size = 0.4, alpha = 0.3) +
  facet_wrap(~pop, ncol = 1) +
  scale_color_manual(values = ch_cols, guide="none") +xlab("Chromosome")+
    ylab("log10(P-value)")+
  geom_hline(yintercept = log10(0.05), linetype = 'dashed', color = 'red', size=0.3) +
  geom_hline(yintercept = -log10(0.05), linetype = 'dashed', color = 'red', size=0.3)+
      ggtitle("P-values for changes in Theta")+
    scale_x_continuous(breaks=chrmax$middle, labels=1:26)+
    theme_bw()
ggsave('../Output/Pi/Shuffle/Changes_in_thetaW.siteshuffle.p-values_PWS.png', width = 7.5, height =11, units = 'in', dpi = 300)

#plot Tajama's D p-value vs. position
ggplot(Datall, aes(POSgen, -log10(tDd.p)*sign(tDd), color = Chromo)) + 
    geom_point(size = 0.4, alpha = 0.3) +
    facet_wrap(~pop, ncol = 1) +
    scale_color_manual(values = ch_cols, guide="none") +xlab("Chromosome")+
    ylab("log10(P-value)")+
    geom_hline(yintercept = log10(0.05), linetype = 'dashed',  color = 'red', size=0.3) +
    geom_hline(yintercept = -log10(0.05), linetype = 'dashed', color = 'red', size=0.3)+
    ggtitle("P-values for changes in Tajima's D")+
    scale_x_continuous(breaks=chrmax$middle, labels=1:26)+
    theme_bw()
ggsave('../Output/Pi/Shuffle/Changes_in_TajimaD.siteshuffle.p-values_PWS.png', width = 7.5, height =11, units = 'in', dpi = 300)

1.3 Find the regions with signfiicant P-values (Outlier regions)

1.3.1 Pi

# Outliers

Pi_outliers<-Datall[tPd.p < 0.05,]
Theta_outliers<-Datall[tWd.p < 0.05,]
TajimaD_outliers<-Datall[tDd.p < 0.05,] #no outliers

# Summary per chromosome per population
pi<-data.frame(table(Pi_outliers$pop, Pi_outliers$Chromo))
the<-data.frame(table(Theta_outliers$pop, Theta_outliers$Chromo))
D<-data.frame(table(TajimaD_outliers$pop, TajimaD_outliers$Chromo))

# Summary per population
pi2<-data.frame(table(Pi_outliers$pop))
the2<-data.frame(table(Theta_outliers$pop))
Ds2<-data.frame(table(TajimaD_outliers$pop))


#plot PWS91-96, 96-07, and 07-17
yrs<-c("PWS91_PWS96","PWS96_PWS07","PWS07_PWS17")
col3<-brewer.pal(5,"PuRd")[c(2,3,5)]
div1<-diverging_hcl(6, palette="Blue-Red")
#reverse the color
div2<-rev(div1)

pis<-pi[pi$Var1 %in% yrs,]
pis$Var1<-factor(pis$Var1, levels=yrs)
ggplot(pis, aes(x=Var2, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(values=col3)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
    ggtitle(expression(paste("Changes in ", pi)))+
    xlab('')+ylab('Number of regions with P<0.05')
ggsave("../Output/Pi/Shuffle/Pi_significant_perChrom_perPop.png", width = 8, height = 4, dpi=300) 

# Per population comparison
ggplot(pi2, aes(x=Var1, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(values=div1)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
    ggtitle(expression(paste("Changes in ", pi)))+
    xlab('')+ylab('Number of regions with P<0.05')
ggsave("../Output/Pi/Shuffle/Pi_significant_perComparison.png", width = 5, height = 4, dpi=300) 

#ordered
pi3<-pi2[order(pi2$Freq, decreasing = T),]
pi3$Var1<-factor(pi3$Var1, levels=paste0(unique(pi3$Var1)))
ggplot(pi3, aes(x=Var1, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(values=div2)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
    ggtitle(expression(paste("Changes in ", pi, " (shuffle)")))+
    xlab('')+ylab('Number of regions with P<0.05')
ggsave("../Output/Pi/Shuffle/Pi_significant_perComparison_ordered.png", width = 5, height = 4, dpi=300) 

#Assign colors to the comparison group
names(div2)<- unique(pi3$Var1)

1.3.2 Theta

#Thetea
ths<-the[the$Var1 %in% yrs,]
ths$Var1<-factor(ths$Var1, levels=yrs)
ggplot(ths, aes(x=Var2, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(values=col3)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
    ggtitle(paste0("Changes in theta"))+
    xlab('')+ylab('Number of regions with P<0.05')
ggsave("../Output/Pi/Shuffle/Theta_significant_perChrom_perPop.png", width = 5, height = 3, dpi=300) 

ggplot(the2, aes(x=Var1, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(values=div1)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
    ggtitle(paste("Changes in theta"))+
    xlab('')+ylab('Number of regions with P<0.05')
ggsave("../Output/Pi/Shuffle/Theta_significant_perComparison.png", width = 5, height = 4, dpi=300) 


the3<-the2[order(the2$Freq, decreasing = T),]
the3$Var1<-factor(the3$Var1, levels=paste0(unique(the3$Var1)))

ggplot(the3, aes(x=Var1, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(name = "Var1",values = div2)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
    ggtitle(paste("Changes in theta"))+
    xlab('')+ylab('Number of regions with P<0.05')
ggsave("../Output/Pi/Shuffle/Theta_significant_perComparison_ordered.png", width = 5, height = 4, dpi=300) 

1.3.3 Tajima’s D - No regions with P < 0.05

# Tajima's D
ggplot(Ds2, aes(x=Var1, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(values=div1)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
    ggtitle(paste0("Changes in Tajima's D"))+
    xlab('')+ylab('Number of regions with P<0.05')
ggsave("../Output/Pi/Shuffle/TajimaD_significant_perComparison.png", width = 5, height = 4, dpi=300) 


D2<-D[D$Var1 %in% yrs,]
D2$Var1<-factor(D2$Var1, levels=yrs)
ggplot(D2, aes(x=Var2, y=Freq, fill=Var1))+
    geom_bar(stat="identity",position=position_dodge(width=0.8))+
    scale_fill_manual(values=col3)+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())+
     ggtitle(paste0("Changes in Tajima's D"))+
    xlab('')+ylab('Number of regions with P>0.05')
#ggsave("../Output/Pi/Shuffle/TajimaD_significant_perChrom_perPop.png", width = 8, height = 4, dpi=300) 

• Most differences exist between 1996 and 2007
• Chr25 has the most significant regions for changes in Pi and Theta

2 Fst genome-scan using a null model

• from Pinsky et al. 2021 https://github.com/pinskylab/codEvol
• Create a null distribution of expected maximum Fst
• Define a genome-wide p-value for each region as (r+1)/(n+1), where r was the number of null simulations with maximum change greater than or equal to the empirical value and n was the number of shuffles

2.1 Shuffle Fst and create a null model of max Fst

• Based on angsd persite Fst output

1. After running angsd (realSFS), print a persite Fst file

```bash
#run FstPWSprint.sh

/home/jamcgirr/apps/angsd/misc/realSFS fst print  /home/ktist/ph/data/angsd/analysis/fst_PWS91_PWS07_persite_maf00.fst.idx > /home/ktist/ph/data/angsd/analysis/fst_PWS91_PWS07_persite_maf00.txt
bgzip /home/ktist/ph/data/angsd/analysis/fst_PWS91_PWS07_persite_maf00.txt

<!-- rnb-source-end -->

<!-- rnb-chunk-end -->


<!-- rnb-text-begin -->


2. Run Fst_shuffle_pws.R at Farm (slurm script: angsd_fst_siteshuffle_null.sh)  


<!-- rnb-text-end -->


<!-- rnb-chunk-begin -->


<!-- rnb-source-begin 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```r
# From https://github.com/pinskylab/codEvol angsd_fst_siteshuffle_null.r

# shuffle ANGSD persite FST A and B values across sites and calculate windowed FST to get a null distribution of max genome-wide FST
# need fst persite output from angsd fst_*_persite_maf00.txt.gz files

# to run on farm


##### R code  ####### 

# parameters
winsz <- 50000 # window size
winstp <- 10000 # window step
nrep <- 1000 # number of reshuffles
minloci <- 10 # minimum number of loci per window to consider


# load functions
require(data.table)


#############
# Prep data
#############
# load fst A/B data
#can <- fread('analysis/Can_40.Can_14.fst.AB.gz')
#setnames(can, c('CHROM', 'POS', 'A', 'B'))

pws9196 <- fread('/home/ktist/ph/data/angsd/analysis/fst_PWS91_PWS96_persite_maf00.txt.gz')
setnames(pws9196, c('CHROM', 'POS', 'A', 'B'))
pws9107 <- fread('/home/ktist/ph/data/angsd/analysis/fst_PWS91_PWS07_persite_maf00.txt.gz')
setnames(pws9107, c('CHROM', 'POS', 'A', 'B'))
pws9117 <- fread('/home/ktist/ph/data/angsd/analysis/fst_PWS91_PWS17_persite_maf00.txt.gz')
setnames(pws9117, c('CHROM', 'POS', 'A', 'B'))
pws9607 <- fread('/home/ktist/ph/data/angsd/analysis/fst_PWS96_PWS07_persite_maf00.txt.gz')
setnames(pws9607, c('CHROM', 'POS', 'A', 'B'))
pws9617 <- fread('/home/ktist/ph/data/angsd/analysis/fst_PWS96_PWS17_persite_maf00.txt.gz')
setnames(pws9617, c('CHROM', 'POS', 'A', 'B'))
pws0717 <- fread('/home/ktist/ph/data/angsd/analysis/fst_PWS07_PWS17_persite_maf00.txt.gz')
setnames(pws0717, c('CHROM', 'POS', 'A', 'B'))

PWS<-list()
PWS[[1]]<-pws9196
PWS[[2]]<-pws9107
PWS[[3]]<-pws9117
PWS[[4]]<-pws9607
PWS[[5]]<-pws9617 
PWS[[6]]<-pws0717 
    
 
# create new columns as indices for windows

for (i in 1: length(PWS)){
    df<-PWS[[i]]
    for(j in 1:(winsz/winstp)){
        df[, (paste0('win', j)) := floor((POS - (j-1)*winstp)/winsz)*winsz + winsz/2 + (j-1)*winstp]
    }
    PWS[[i]]<-df
}

# mark windows with < minloci for removal
rem <- rep(0, 6) # number of windows removed for each of the 6 comparisons

for(i in 1: length(PWS)){
    pw<-PWS[[i]]
    for(j in 1:(winsz/winstp)){
        pwwin <- pw[, .(nsnps = length(POS)), by = .(win = get(paste0('win', j)))] # calc num snps per window
        rem[1] <- rem[1] + pwwin[, sum(nsnps < minloci)] # record number to be removed
        pwwin[, (paste0('win', j, 'keep')) := 1] # create col to mark which windows to keep
        pwwin[nsnps < minloci, (paste0('win', j, 'keep')) := 0] # mark windows to remove
        pwwin[, nsnps := NULL] # drop column
        setnames(pwwin, "win", paste0('win', j)) # change col name
        pw <- merge(pw, pwwin, by = paste0('win', j), all.x = TRUE) # merge keeper col back to full dataset
    }
    PWS[[i]]<-pw
}

rem # number of windows removed for each comparison




####################################
# shuffle and recalc windowed FST
####################################
colnms <- c('CHROM', 'POS', paste0('win', 1:(winsz/winstp)), paste0('win', 1:(winsz/winstp), 'keep')) # list of column names we want out of the base data.table

# PWS07-17
pops<-c("PWS91.96","PWS91.07","PWS91.17","PWS96.07","PWS96.17","PWS07.17")


for(p in 1:length(PWS)){
    print(paste0('Starting ', pops[p]))

    pw<-PWS[[p]]
    for(i in 1:nrep){
        cat(i); cat(' ')
        # create new dataset
        inds <- sample(1:nrow(pw), nrow(pw), replace = FALSE)
        temp <- cbind(pw[, ..colnms], pw[inds, .(A, B)]) # shuffle FSTs across positions
        
        # calc fst for each window to keep
        for(j in 1:(winsz/winstp)){
            temp2 <- temp[get(paste0('win', j, 'keep')) == 1, ] # trim to windows to keep. can't combine with next line for some reason.
            if(j ==1) tempfsts <- temp2[, .(fst = sum(A)/sum(B)), by = .(CHROM, POS = get(paste0('win', j)))]
            if(j > 1) tempfsts <- rbind(tempfsts, temp2[, .(fst = sum(A)/sum(B)), by = .(CHROM, POS = get(paste0('win', j)))])
        }
        
        # save the max windowed fst
        # exclude windows with negative midpoints
        if(i == 1) maxfst <- tempfsts[POS > 0, max(fst, na.rm = TRUE)]  
        if(i > 1) maxfst <- c(maxfst, tempfsts[POS > 0, max(fst, na.rm = TRUE)])
    }

    print(paste('Max:', max(maxfst, na.rm = TRUE), '; 95th:', quantile(maxfst, prob = 0.95, na.rm = TRUE)))
    
    write.csv(maxfst, gzfile(paste0('/home/ktist/ph/data/angsd/analysis/',pops[p], '_siteshuuffle.csv.gz')), row.names = FALSE)
    rm(maxfst)
}

2.2 Assess the results from site reshuffled Fst

Need - sitehuffle results fst_siteshuuffle.csv.gz - window-based Fst results from angsd _50kWindow_maf00 - persite Fst files after LD pruning (with AB info) *_persite_maf00_ldtrim.csv.gz

#from https://github.com/pinskylab/codEvol

# parameters
minloci <- 10 
winsz <- 50000 # window size
winstp <- 10000 # window step

# load functions
require(data.table)
require(ggplot2)

calcp <- function(fst, null) return((sum(null > fst)+1)/(length(null)+1)) # equation from North et al. 2002 Am J Hum Gen

# read in and prep data
years<-c("PWS91","PWS96","PWS07","PWS17")
comb<-t(combn(years, 2))

# continuous nucleotide position for the whole genome
chrmax <- fread('../Data/new_vcf/chr_sizes.bed')
chrmax<-chrmax[,-2]
colnames(chrmax)<-c("chr", "len")
chrmax$start<-c(0,cumsum(chrmax$len)[1:(nrow(chrmax)-1)])
setkey(chrmax, chr)

prunedFst_gw<-data.frame(pop1=comb[,1],pop2=comb[,2])
#for (p in 1: nrow(comb)){
    for (p in 1:5){
    #genome-wide max Fst from reshuffling (unlinked sites)
    null<-fread(paste0('Data/shuffle/', comb[p,1],".",comb[p,2],'_fst_siteshuuffle.csv.gz'))
    #window-based Fst from angsd            
    fstwin <- fread(paste0('Data/new_vcf/angsd/fromVCF/2D/fst_',comb[p,1],"_",comb[p,2],'_50kWindow_maf00'), header = FALSE, col.names = c('region', 'chr', 'midPos', 'Nsites', 'fst')) # all sites
    #persite fst (AB) -pruned sites
    AB <- fread(paste0('Data/shuffle/fst_',comb[p,1],"_",comb[p,2],'_persite_maf00_ldtrim.csv.gz'))
    
    # merge nucleotide position into the frequency files
    setkey(AB, CHROM)
    AB <- AB[chrmax[, .(CHROM = chr, start)], ]
    AB[, posgen := POS + start]
    AB[,start := NULL]
    
    # Calc genome-wide FST
    prunedFst_gw$gwFst[p]<-AB[!is.na(A), sum(A)/sum(B)]
    
    # Calc windowed FST
    # create new columns as indices for windows
    for(j in 1:(winsz/winstp)){
        AB[, (paste0('win', j)) := floor((POS - (j-1)*winstp)/winsz)*winsz + winsz/2 + (j-1)*winstp]
    }
    
    # calc fst and # snps per window
    for(j in 1:(winsz/winstp)){
        if(j ==1){
            fstwin <- AB[, .(fst = sum(A)/sum(B), nloci = length(POS)), by = .(CHROM, midPos = get(paste0('win', j)))]
        } 
        if(j > 1){
            fstwin <- rbind(fstwin, AB[, .(fst = sum(A)/sum(B), nloci = length(POS)), by = .(CHROM, midPos = get(paste0('win', j)))])
        } 
    }
    
    ## null model stats
    fstats<-null[, .(max = max(x), u95 = quantile(x, probs = 0.95))]
    prunedFst_gw$null.Fstmax[p]<-fstats$max[1]
    prunedFst_gw$null.Fst.95q[p]<-fstats$u95[1]
    
    #Calculate p-values
    pval<-fstwin[, p := calcp(fst, null$x), by = .(CHROM, midPos)]
    
    #combined the datasets
    pair<-paste0(comb[p,1],"_",comb[p,2])
    fstwin[, pop := pair ]
    write.csv(fstwin, paste0("../Output/Fst/fst_siteshuffle.pairwise_", pair,".csv"))
}

write.csv(prunedFst_gw, "../Output/Fst/fst_siteshuffle_pws_summary.csv")

data<-data.frame()
for(i in 1: nrow(comb)){
    pair<-paste0(comb[i,1],"_",comb[i,2])
    df<-fread(paste0("../Output/Fst/fst_siteshuffle.pairwise_", pair,".csv"))
    df<-df[!is.na(fst) & midPos > 0, ]
    df[,ch:= as.integer(gsub("chr",'', CHROM))]
    setkey(df,CHROM)
    df<-df[chrmax[, .(CHROM = chr, start)], ]
    df[,pos.gw:= midPos+start]
    #setkey(df, ch, midPos)
    data<-rbind(data, df)
}

write.csv(data, file = gzfile('../Output/Fst/fst_siteshuffle.angsd.PWS.csv.gz'), row.names = FALSE)

2.3 Plot the results

data<-fread('../Output/Fst/fst_siteshuffle.angsd.PWS.csv.gz')

#pop as factor 
data[, pop := factor(pop, levels = c("PWS91_PWS96","PWS91_PWS07","PWS91_PWS17","PWS96_PWS07","PWS96_PWS17","PWS07_PWS17"))]

# plot p-value vs. position
two_cols<-rep(c("steelblue","lightblue"), times=13)
minloci <- 10 # minimum number of loci per window to consider

ggplot(data[nloci >= minloci, ], aes(pos.gw, -log10(p), color = factor(ch))) + 
    geom_point(size = 0.2, alpha = 0.5) +
    facet_wrap(~pop, ncol = 1) +
    scale_color_manual(values = two_cols, guide='none') +
    geom_hline(yintercept = -log10(0.05), linetype = 'dashed', color = 'grey')+
    theme_bw()+
    theme(axis.text.x = element_blank())+
    xlab("Genome")
ggsave("../Output/Fst/fst.siteshuffle.p_vs_pos.PWS.png", width = 7.5, height = 7.5,dpi = 300)

• Number of loci per window vs. Fst p-values

# plot p-value vs. nloci to check if any biases exist
ggplot(data, aes(nloci, -log10(p), color = pop)) + 
    geom_point(size = 0.6, alpha = 0.5) +
    geom_hline(yintercept = -log10(0.05), linetype = 'dashed', color = 'grey') + 
    scale_x_log10()+theme_bw()+theme(legend.title = element_blank())+
    guides(color = guide_legend(override.aes = list(size = 3, alpha=1)))
ggsave("../Output/Fst/fst.siteshuffle.p_vs_nloci.PWS.png", width = 8, height =4,dpi = 300)

2.4 Significant outlier regions

2.4.1 p-value < 0.05

```r
outliers<-data[p < 0.05, ]
write.csv(outliers, \../Output/Fst/Fst_nullshuffling_outliers_PWS.csv\)

counts<-data.table(table(outliers$pop))
ggplot(counts, aes(x=V1, y=N))+
    geom_bar(stat=\identity\, fill=cols[4])+
    xlab('')+ylab('')+
    theme_classic()+
    theme(axis.text.x = element_text(angle=45, hjust=1))
ggsave(\../Output/Fst/Fst_outliers_byComparison.png\, width = 4, height = 3, dpi=300 )


counts$V1<-factor(counts$V1, levels=c(\PWS96_PWS07\,\PWS07_PWS17\,\PWS91_PWS96\, \PWS91_PWS07\, \PWS91_PWS17\,\PWS96_PWS17\))
ggplot(counts, aes(x=V1, y=N, fill=V1))+
    geom_bar(stat=\identity\)+
    scale_fill_manual(name = \V\,values = div2)+
    xlab('')+ylab('Number of regions with P<0.05')+
    theme_classic()+ggtitle(\Fst (shuffle)\)+
    theme(axis.text.x = element_text(angle=45, hjust=1), legend.title = element_blank())
ggsave(\../Output/Fst/Fst_outliers_byComparison_ordered.png\, width = 4, height = 3, dpi=300 )



#outliers<-read.csv(\../Output/Fst/Fst_nullshuffling_outliers_PWS.csv\, row.names = 1)
knitr::kable(outliers[,c(2,3,4,5,6,7,8)], caption=\Outlier regions\)

#Outlier regions
#CHROM  midPos  fst nloci   p   pop ch
#chr25  825000  0.1210997   138 0.003996    PWS96_PWS07 25
#chr25  835000  0.0818802   279 0.020979    PWS96_PWS07 25
#chr25  845000  0.0721926   311 0.033966    PWS96_PWS07 25
#chr25  805000  0.1242652   166 0.002997    PWS96_PWS07 25
#chr25  815000  0.1377218   155 0.002997    PWS96_PWS07 25
#chr19  1375000 0.1251602   42  0.003996    PWS07_PWS17 19

```

2.4.2 Top 1% outliers & P< 0.2

• relaxing the cutoff

* NO overlapping regions from PCAngsd selection scan